Chapter 2.6, Problem LC

(a)

To determine

To calculate: Formula for the mass of a planet according to Kepler granted that the mass of a planet with a satellite is directly proportional to the cube of the mean distance from the satellite to the planet, and inversely proportional to the square of the period of revolution.

(b)

To determine

To calculate: The proportionality constant using the observations and estimates for the earth and the moon granted that the mass of the earth,$m=5.976\times {10}^{24}\text{kg}$, and the period of revolution, $p=27.322\text{days}$ and distance, $d=384.4\times {10}^3\text{km}$

(c)

To determine

To calculate: The mass of the Mars granted that the period of revolution, $p=7.65$ hours or $p=\frac{7.65}{24}$ days, the distance, $d=9330\text{km}$ and and the proportionality constant, $k=7.8593\times {10}^{10}$.

(d)

To determine

To calculate: The approximate ratio of the mass of the earth to the mass of Mars granted that the Mass of the earth,$m_1=5.976\times {10}^{24}\text{kg}$ and the mass of the Mars, $m_2=6.278\times {10}^{23}\text{kg}$

(e)

To determine

To calculate: The mean distance between Io and the Jupiter granted that the mass of the Jupiter, $m=1.921\times {10}^{27}\text{kg}$ and the period of revolution, $p=42.47$ hours or $p=\frac{42.47}{24}$ days